Lutfiye Durak-Ata

The discrete fractional Fourier transform based on the DFT matrix

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yet-elegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT. By appropriately combining existing commuting matrices we obtain a new commuting matrix which performs better. We show the validity of the proposed algorithms by computer simulations comparing DFrFT points and continuous FrFT samples for various signals.

Efficient computation of DFT commuting matrices by a closed-form infinite order approximation to the second differentiation matrix

In order to define the discrete fractional Fourier transform, Hermite Gauss-like eigenvectors are needed and one way of extracting these eigenvectors is to employ DFT commuting matrices. Recently, Pei et al. exploited the idea of obtaining higher order DFT-commuting matrices, which was introduced by Candan previously. The upper bound of O(h^2^k) approximation to NxN commuting matrix is 2k+1@?N in Candans work and Pei et al. improved the proximity by removing this upper bound at the expense of higher computational cost. In this paper, we derive an exact closed form expression of infinite-order Taylor series approximation to discrete second derivative operator and employ it in the definition of excellent DFT commuting matrices. We show that in the limit this Taylor series expansion converges to a trigonometric function of second-order differentiating matrix. The commuting matrices possess eigenvectors that are closer to the samples of Hermite-Gaussian eigenfunctions of DFT better than any other methods in the literature with no additional computational cost.

PWVD resolution considerations for LFMCW signal detection by WHT

Linear Frequency Modulated Continuous Waveform (LFMCW) is one of the most common waveforms used in low probability of intercept (LPI) radars. The Wigner-Hough transform (WHT) is a powerful technique for detection and parameter extraction of LFMCW waveforms that can be employed by Electronic Support Receivers. For a fast detection and a timely response to the adversary emitter, the selection of the pseudo Wigner-Ville distribution (PWVD) window length is critical. In this work we analyze the relation between PWVD window length, WHT span angle and span resolution. It is shown that faster correct detections can be achieved by decreasing the PWVD window length and consequently decreasing the WHT plane. A rapid detection and apiori estimation of target emitter signal chirp rate will allow enough time for a fine tuned post-processing which can be applied specifically to the a priori estimates.

Dispersed chirp-z transform-based spectrum sensing and utilisation in cognitive radio networks

The authors propose novel spectrum sensing and utilisation schemes for cognitive radio networks using the chirp-z transform. To improve the spectral efficiency, a dispersed chirp-z transform is introduced with the energy detection method. The dispersed chirp-z transform enables one to analyse the dispersed frequency spectrum of any frequency range of interest. The analysis is first focused on the sensing part, including the derivations of closed-form expressions for the optimal detection thresholds minimising the total error rate over additive white Gaussian noise (AWGN), Rayleigh, Rician and log-normally distributed fading channels. Then, the performance analysis of the proposed system is investigated for efficient spectrum utilisation over AWGN and fading channels by presenting the receiver operating characteristics. Conventional and segmented chirp-z transform-based spectrum utilisation techniques are also introduced for performance comparison purposes. Finally, the theoretical framework and the optimal threshold derivations through simulations are verified. The analyses reveal that the proposed schemes have a considerable potential to improve the non-cooperative spectrum sensing and utilisation performance.

Defining the effective threshold using modified wigner-hough transform in FMCW-signal detection

In response to the fast improvements in anti-radiation systems and electronic attack systems, radar systems began exploiting low power, wide-band, frequency agility techniques to decrease their intercept probability. This increase in the use of low probability of intercept (LPI) waveforms in current radar systems enforces the intercept receiver to use sophisticated signal processing algorithms. It has been observed that, the threshold applied on Wigner-Ville images has an impact on the efficiency of Wigner-Hough based algorithms. In this study, we investigated the effect of the WV threshold on signals with SNRs ranging from [0dB, -9dB], and suggested that the optimum threshold is between 20-40% of the max WV image energy intensity.

Partial spectrum utilization for energy detection in cognitive radio networks

This paper proposes the use of chirp-z transform (CZT) in spectrum sensing to achieve higher frequency resolution in spectrum monitoring. The CZT method can efficiently utilize the dispersed frequency spectrum of any desired band of interest. The performance of the proposed system over additive white Gaussian noise (AWGN) and Rayleigh channels is analyzed and presented through ROC curves. In order to maximize the total error rate performance of the proposed system, the optimal detection threshold expressions are derived in the case of AWGN and Rayleigh faded channels. Afterwards, the optimal detection threshold expressions are validated by simulation and numerical results.

Spectrally efficient OFDMA lattice structure via toroidal waveforms on the time-frequency plane

We investigate the performance of frequency division multiplexed (FDM) signals, where multiple orthogonal Hermite-Gaussian carriers are used to increase the bandwidth efficiency. Multiple Hermite-Gaussian functions are modulated by a data set as a multicarrier modulation scheme in a single time-frequency region constituting toroidal waveform in a rectangular OFDMA system. The proposed work outperforms in the sense of bandwidth efficiency compared to the transmission scheme where only single Gaussian pulses are used as the transmission base. We investigate theoretical and simulation results of the proposed methods.

Optimal Detection Thresholds in Spectrum Sensing with Receiver Diversity

We investigate the performance of receiver diversity techniques by considering energy detector based optimal spectrum sensing in cognitive radio networks over Rayleigh fading channel for both non-cooperative and cooperative communication systems. The analysis is first focused on the non-cooperative spectrum sensing part, including the analyses of selection combining (SC), equal gain combining (EGC), and maximal ratio combining (MRC) receiver diversity systems. We derive exact closed-form expressions for the optimal detection thresholds for each diversity scheme. By using these expressions, we present their detection performance compared to the no-diversity case. Then in the second part of this paper, the performance analysis of the proposed system is investigated for amplify-and-forward relaying spectrum sensing with SC, EGC, and MRC diversity techniques in Rayleigh fading channels. Particularly, average detection probability of end-to-end signal-to-noise ratio for SC and EGC schemes and the exact closed-form expressions of the optimal detection threshold for SC, EGC, and MRC schemes are derived. We also present detection performance for the cooperative system compared to the non-cooperative one. The analyses are validated by simulated receiver operating characteristic curves.

Chirp Z transform based spectrum sensing via energy detection

In this study, the performance analysis of Fast Fourier Transform and Chirp Z transform based OFDM systems for cognitive radio networks with energy detector model for the spectrum sensing method is realized. Here, energy detection model for noncooperative spectrum sensing is investigated. On the other hand, the analysis is implemented by segmented Chirp z transform. In this study Chirp z transform based spectrum sensing is proposed for the increase of dispersed spectrum utilization and in this context firstly used in literature. Also with the system model, using inverse fast Fourier transform in transmitter and Chirp z transform in receiver rather than fast Fourier transform, the computational complexity and the processing time are reduced, and performance increase is observed for high signal to noise ratio values.

Spectrum sensing for cognitive radio with selection combining receiver antenna diversity

In this study the performance analysis of energy detector method for the spectrum sensing model in cognitive radio networks over Rayleigh fading channel with selection combining of the receiver diversity technique is examined. Here, energy detector model for non-cooperative spectrum sensing is investigated in which Chirp-z transform is used. The Chirp-z transform is proposed as an efficient algorithm to increase the dispersed frequency spectrum utilization, provides a flexibility to work only on the frequency spectrum of interest. The general closed form mathematical equation of the optimal detection threshold for selection combining receiver diversity technique is derived over Rayleigh fading channel. The performance analysis of the proposed system model is investigated with the optimal detection threshold value and presented through ROC curve for different SNR values. The achieved results validate the spectrum sensing performance increase in selection combining of the receiver antenna diversity technique, compared to the no diversity case.